2x^2+10x-1010=0

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Solution for 2x^2+10x-1010=0 equation: 


Simplifying
2x2 + 10x + -1010 = 0

Reorder the terms:
-1010 + 10x + 2x2 = 0

Solving
-1010 + 10x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-505 + 5x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-505 + 5x + x2)' equal to zero and attempt to solve:

Simplifying
-505 + 5x + x2 = 0

Solving
-505 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '505' to each side of the equation.
-505 + 5x + 505 + x2 = 0 + 505

Reorder the terms:
-505 + 505 + 5x + x2 = 0 + 505

Combine like terms: -505 + 505 = 0
0 + 5x + x2 = 0 + 505
5x + x2 = 0 + 505

Combine like terms: 0 + 505 = 505
5x + x2 = 505

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 505 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 505 + 6.25

Combine like terms: 505 + 6.25 = 511.25
6.25 + 5x + x2 = 511.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 511.25

Calculate the square root of the right side: 22.610838109

Break this problem into two subproblems by setting 
(x + 2.5) equal to 22.610838109 and -22.610838109.


Subproblem 1
x + 2.5 = 22.610838109

Simplifying
x + 2.5 = 22.610838109

Reorder the terms:
2.5 + x = 22.610838109

Solving
2.5 + x = 22.610838109

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 22.610838109 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 22.610838109 + -2.5
x = 22.610838109 + -2.5

Combine like terms: 22.610838109 + -2.5 = 20.110838109
x = 20.110838109

Simplifying
x = 20.110838109


Subproblem 2
x + 2.5 = -22.610838109

Simplifying
x + 2.5 = -22.610838109

Reorder the terms:
2.5 + x = -22.610838109

Solving
2.5 + x = -22.610838109

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -22.610838109 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -22.610838109 + -2.5
x = -22.610838109 + -2.5

Combine like terms: -22.610838109 + -2.5 = -25.110838109
x = -25.110838109

Simplifying
x = -25.110838109


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {20.110838109, -25.110838109}
Solution
x = {20.110838109, -25.110838109}

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